President Donald Trump is "all in" on the newly released Republican health-care bill, a White House official told CNBC on Tuesday.

"Hundred percent," the official added.

CNBC's Eamon Javers tweeted Tuesday morning.

Trump also tweeted about the Republican plan Tuesday morning.

Meanwhile, Mick Mulvaney, the new director of the Office of Management and Budget, told NBC on Tuesday the GOP plan to replace Obamacare gives all Americans access to affordable coverage.

House Republicans on Monday night unveiled their plan for repealing and replacing former President Barack Obama's Affordable Care Act. It would kill the individual mandate, but keep pre-existing condition protections and the under-26 age limit for young adults to stay covered by their parents. The GOP plan would also alter the way many customers get access to financial aid to help them pay for insurance.

Rep. Mick Mulvaney (R-SC)

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Mulvaney, who emerged as a key White House liaison with Capitol Hill on health care, said on the "TODAY" show Tuesday it's unfair to compare the GOP's American Health Care Act to the promise of Obama's health-care law.

"I don't think it's fair to want to compare what we're proposing ... to what Obamacare might have been. You have to compare it to what Obamacare is, and it's a failure," Mulvaney said. "By that comparison, this program is going to be a great success."

Asked whether all Americans would get health coverage under the Republican plan, Mulvaney told NBC, "What people are getting here is access to coverage that they don't have now."

"What Obamacare did was make insurance affordable, but care impossible to actually afford. The deductibles are simply too high. So folks could say they have full coverage, but they couldn't actually get the medical care they needed when they get sick," he said. "We solve that by giving everyone access to health care they can actually afford."

The nonpartisan Congressional Budget Office has not analyzed how much the GOP's proposal will cost.

"[But] we will know what it costs before they vote on it," Mulvaney said, predicting "this is going to save a dramatic amount of money" and be helpful to the deficit in the long term.

The House Ways and Means Committee and Energy and Commerce Committee are set to start the process of marking up the measure this week.